Roesser form of (wave) linear repetitive processes and structural stability

Abstract

We use the algebraic analysis approach to multi- dimensional systems theory to study (wave) linear 2D discrete repetitive processes. In a previous work, we have proved that every linear 2D discrete repetitive process can be transformed into an equivalent (in the sense of algebraic analysis) explicit Roesser model. In the present paper we first investigate the conservation of the important notion of structural stability via this equivalence transformation. Then we extend the previous results to wave linear repetitive processes: we prove that such a general model can always be transformed into an equivalent implicit Roesser model which may be used to study stability properties of wave linear repetitive processes.